Stochastic simulation model for tropical cyclone tracks, with special emphasis on landfall behavior

We consider a spatial stochastic model for the simulation of tropical cyclone tracks, which has recently been introduced. Cyclone tracks are represented as labeled polygonal lines, which are described by the movement directions, translational speeds, and wind speeds of the cyclones in regular 6-h intervals. In the present paper, we compare return levels for wind speeds of historically observed cyclone tracks with those generated by the simulator, where a mismatch is shown for most of the considered coastal regions. To adjust this discrepancy, we develop a stochastic algorithm for acceptance and rejection of simulated cyclone tracks with landfall. It is based on the fact that the locations, translational speeds, and wind speeds of cyclones at landfall constitute three-dimensional Poisson point processes, which are a basic model type in stochastic geometry. Due to that, a well-known thinning property of Poisson processes can be applied. This means that to each simulated cyclone, an acceptance probability is assigned, which is higher for cyclones with suitable landfall characteristics and lower for implausible ones. More intuitively, the algorithm comprises the simulation of a more comprehensive cyclone event set than needed and the random selection of those tracks that best match historical observations at landfall. A particular advantage of our algorithm is its applicability to multiple landfalls, i.e., to cyclones that successively make landfall at two geographically distinct coastlines, which is the most relevant case in applications. It turns out that the extended simulator provides a much better accordance between landfall characteristics of historical and simulated cyclone tracks.